Question: A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals. If both lights start flashing at the same time, how many times do they flash together in each hour?
- 29
- 30
- 31
- 32
- 33
Correct Answer: B
Solution and Explanation
Approach Solution 1:
Hint: To solve this question first we need to calculate the time interval of red light and green light for one minute. Next by doing the LCM for both red and green lights, we will find the final answer.
This above given sum is the time and second math. It is given that the red light flashes for the first time every 60 seconds. So to calculate the 3 given intervals it becomes 60/3= 20 seconds.
So, the flash at every 20 seconds becomes equal to 20 sec,40sec,60sec,80sec,100sec,120 sec,
and so on (these are the multiples of 20)
Similarly, for the case of the green light will flash for the first time in two minutes after 120/5=24sec
Hence, it will flash at an interval of 24 sec each time equals to 24sec, 48sec, 72sec, 96 sec, 120sec, 144 sec and so on (these are the multiples of 24)
Now taking the common multiple of both red and green light that equals 120. So, simply doing the LCM of 20 and 24 equals 120. Thereafter both the lights will flash together for the first time in 120 seconds.
As 1 hour = 3600 seconds
Therefore the number of intervals of 120 seconds in one hour is
So, 3600/120=30
Therefore, these two lights will flash together 30 times in each hour.
So, the required correct answer is option C.
Note: In solving such problems, we need to find the two different events with different time intervals at the same time. A tip is to do the LCM of both times as LCM is the first occurrence where both the events happen together.
Approach Solution 2:
Here is the shortcut to solve the above given problem. We can simply calculate the red light flashes 3 times every minute. This makes 60/3=20 seconds.
So, the same for the green light flashes 5 times every 2 minutes. This makes 120/5=24 seconds.
So, taking the LCM of 20 and 24 to calculate the total number of flashes makes it 120 seconds- 2 minutes. Hence, the number of flashes in 1 hour = 2*60 = 30.
So, the required correct answer is option C.
Approach Solution 3:
Given statement: a red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals.
The red light will flash for the first time in one minute after 60/3= 20sec
That means it will flash at an interval of 20 sec each time
=20sec,40sec,60sec,80sec,100sec,120sec and so on (multiples of 20)
Similarly the green light will flash for the first time in two minutes after 120/5= 24sec1205=24sec
That means it will flash at an interval of 24 sec each time
=24sec,48sec,72sec,96sec,120sec,144sec and so on (multiples of 24)
Now take the common multiple of both red and green light which is =120
Which can also be done by simply taking the LCM of 20 and 24 = 120
Therefore both the lights will flash together for the first time in 120 sec
As we know
An hour has 3600 sec.
Therefore the number of intervals of 120 seconds in one hour is 3600/120= 30
Hence, these two lights will flash together 30 times in each hour.
“A red light flashes 3 times per minute and a green light flashes 5 times in two minutes at regular intervals.”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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